Subgroups — #28404320

Order 14464.

1022 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20299319	C₂	1	2	yes	maximal, complemented
2	#20299306	C₂	1	2	yes	maximal, complemented
3	#20299290	C₂	1	2	yes	maximal, complemented
4	#20299283	C₂	1	4	yes	maximal, complemented
5	#20299282	C₂	1	2	yes	maximal, complemented
6	#20299274	C₂	1	4	yes	maximal, complemented
7	#20299229	C₂	1	1	yes	maximal, characteristic, complemented
8	#20299221	C₂	1	2	yes	maximal, complemented
9	#20299208	C₂	1	2	yes	maximal, complemented
10	#20299172	C₂	1	1	yes	maximal, characteristic, complemented
11	#20299150	C₂	1	2	yes	maximal, complemented
12	#20299134	C₂	1	2	yes	maximal, complemented
13	#20299109	C₂	1	1	yes	maximal, characteristic
14	#20299079	C₂	1	1	yes	maximal, characteristic, complemented
15	#20299076	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#16813581	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₂²⋊Q₈×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#14268647	C₂²	1	1	yes	characteristic
19	#16813621	C₂²	1	2	yes	complemented
20	#16813621	C₂²	1	2	yes	complemented
21	#16813620	C₂²	1	2	yes	complemented
22	#16813617	C₂²	1	4	yes	complemented
23	#16813617	C₂²	1	4	yes	complemented
24	#16813615	C₂²	1	4	yes	—
25	#16813615	C₂²	1	4	yes	—
26	#16813613	C₂²	1	2	yes	complemented
27	#16813613	C₂²	1	4	yes	complemented
28	#16813613	C₂²	1	2	yes	complemented
29	#16813612	C₂²	1	4	yes	complemented
30	#16813612	C₂²	1	4	yes	complemented
31	#16813611	C₂²	1	2	yes	complemented
32	#16813608	C₂²	1	4	yes	—
33	#16813606	C₂²	1	4	yes	—
34	#16813605	C₂²	1	4	yes	—
35	#16813605	C₂²	1	2	yes	—
36	#16813604	C₂²	1	4	yes	—
37	#16813602	C₂²	1	4	yes	complemented
38	#16813601	C₂²	1	4	yes	—
39	#16813601	C₂²	1	1	yes	characteristic
40	#16813601	C₂²	1	1	yes	characteristic
41	#16813599	C₂²	1	4	yes	—
42	#16813598	C₂²	1	2	yes	complemented
43	#16813598	C₂²	1	2	yes	complemented
44	#16813596	C₂²	1	1	yes	characteristic
45	#16813596	C₂²	1	1	yes	characteristic
46	#16813591	C₂²	1	2	yes	—
47	Q₈×Dic₁₁₃	C₂²	1	2	yes	complemented
48	Q₈×Dic₁₁₃	C₂²	1	2	yes	complemented
49	Q₈×Dic₁₁₃	C₂²	1	2	yes	complemented
50	Q₈×Dic₁₁₃	C₂²	1	2	yes	complemented
51	#16813587	C₂²	1	4	yes	complemented
52	#16813587	C₂²	1	2	yes	complemented
53	#16813584	C₂²	1	2	yes	complemented
54	C₄×C₂²⋊D₁₁₃	C₂²	1	4	yes	—
55	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
56	C₄×C₂²⋊D₁₁₃	C₂²	1	2	yes	—
57	#16813582	C₂²	1	4	yes	—
58	#16813581	C₂²	1	4	yes	—
59	#16813581	C₂²	1	1	yes	characteristic
60	#16813581	C₂²	1	2	yes	—
61	#16813581	C₂²	1	1	yes	characteristic
62	#16813581	C₂²	1	1	yes	characteristic
63	#16813581	C₂²	1	1	yes	characteristic
64	#16813581	C₂²	1	2	yes	—
65	#16813581	C₂²	1	1	yes	characteristic
66	#16813580	C₂²	1	4	yes	complemented
67	#16813580	C₂²	1	2	yes	complemented
68	#16813578	C₂²	1	4	yes	—
69	C₂×C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
70	C₂×C₄⋊Dic₁₁₃	C₂²	1	1	yes	characteristic
71	C₄⋊C₄×D₁₁₃	C₂²	1	2	yes	complemented
72	C₂×C₂²⋊Dic₁₁₃	C₂²	1	2	yes	—
73	C₂×C₄×Dic₁₁₃	C₂²	1	2	yes	—
74	C₂²×Q₈×C₁₁₃	C₂²	1	1	yes	characteristic
75	C₂³×C₄×C₁₁₃	C₂²	1	1	yes	characteristic
76	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	—
77	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	—
78	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	—
79	C₂²⋊Q₈×C₁₁₃	C₂²	1	2	yes	—
80	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	2	yes	—
81	C₂×C₄⋊C₄×C₁₁₃	C₂²	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₁₁₃	C₂²	1	2	yes	—
83	#14268647	—	2	4	no	—
84	C₂×Dic₂₂₆	C₂³	1	1	yes	characteristic
85	C₂×Dic₂₂₆	C₂³	1	4	yes	—
86	C₂×D₄₅₂	C₂³	1	1	yes	characteristic
87	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
88	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
89	C₂×C₂²⋊D₁₁₃	C₂³	1	2	yes	—
90	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
91	C₂²×Dic₁₁₃	C₂³	1	2	yes	—
92	C₂×C₄×D₁₁₃	C₂³	1	2	yes	—
93	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
94	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
95	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
96	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
97	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
98	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
99	C₄⋊Dic₁₁₃	C₂³	1	2	yes	—
100	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
101	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
102	C₄⋊Dic₁₁₃	C₂³	1	1	yes	characteristic
103	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
104	C₄⋊Dic₁₁₃	C₂³	1	4	yes	—
105	#14268626	C₂³	1	4	yes	—
106	#14268626	C₂³	1	4	yes	—
107	#14268626	C₂³	1	4	yes	—
108	#14268626	C₂³	1	4	yes	—
109	#14268626	C₂³	1	2	yes	—
110	#14268626	C₂³	1	2	yes	—
111	#14268626	C₂³	1	4	yes	—
112	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
113	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
114	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
115	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
116	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
117	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
118	C₂²⋊Dic₁₁₃	C₂³	1	2	yes	—
119	#14268624	C₂³	1	2	yes	—
120	#14268624	C₂³	1	4	yes	—
121	#14268624	C₂³	1	4	yes	—
122	#14268624	C₂³	1	4	yes	—
123	#14268624	C₂³	1	2	yes	—
124	C₄×Dic₁₁₃	C₂³	1	2	yes	—
125	C₄×Dic₁₁₃	C₂³	1	2	yes	—
126	C₄×Dic₁₁₃	C₂³	1	2	yes	—
127	C₄×Dic₁₁₃	C₂³	1	2	yes	—
128	C₄×Dic₁₁₃	C₂³	1	4	yes	—
129	C₄×Dic₁₁₃	C₂³	1	4	yes	—
130	C₄×Dic₁₁₃	C₂³	1	4	yes	—
131	C₄×Dic₁₁₃	C₂³	1	2	yes	—
132	C₂⁴×C₁₁₃	C₂³	1	1	yes	characteristic
133	C₂×Q₈×C₁₁₃	—	2	4	no	—
134	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
135	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
136	C₂²×C₄×C₁₁₃	—	2	4	no	—
137	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
138	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
140	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
141	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
142	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
143	C₂²×C₄×C₁₁₃	C₂³	1	2	yes	—
144	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
145	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
146	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
147	C₄⋊C₄×C₁₁₃	C₂³	1	2	yes	—
148	C₄⋊C₄×C₁₁₃	C₂³	1	4	yes	—
149	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
150	C₂²⋊C₄×C₁₁₃	C₂³	1	4	yes	—
151	C₂³×C₁₁₃	—	2	2	no	—
152	C₂³×C₁₁₃	—	2	2	no	—
153	C₂³×C₁₁₃	—	4	1	no	—
154	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
155	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
156	C₂³×C₁₁₃	C₂⁴	1	1	yes	characteristic
157	C₂²×D₁₁₃	C₂⁴	1	2	yes	—
158	Q₈×C₁₁₃	—	2	4	no	—
159	Q₈×C₁₁₃	—	2	4	no	—
160	C₂×C₄×C₁₁₃	—	2	2	no	—
161	C₂×C₄×C₁₁₃	—	2	4	no	—
162	C₂×C₄×C₁₁₃	—	2	2	no	—
163	C₂×C₄×C₁₁₃	—	2	2	no	—
164	C₂×C₄×C₁₁₃	—	2	2	no	—
165	C₂×C₄×C₁₁₃	—	2	2	no	—
166	C₂×C₄×C₁₁₃	—	4	2	no	—
167	C₂×C₄×C₁₁₃	#41	1	4	yes	—
168	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
169	C₂×C₄×C₁₁₃	C₂⁴	1	4	yes	—
170	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
171	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
172	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
173	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
174	C₂²⋊D₁₁₃	—	2	4	no	—
175	C₂²⋊D₁₁₃	—	2	4	no	—
176	C₂²⋊D₁₁₃	—	4	2	no	—
177	C₂×Dic₁₁₃	—	2	4	no	—
178	C₂×Dic₁₁₃	—	4	2	no	—
179	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
180	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
181	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
182	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
183	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
184	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
185	C₂×Dic₁₁₃	C₂⁴	1	2	yes	—
186	D₄₅₂	—	2	2	no	—
187	C₄×D₁₁₃	—	2	4	no	—
188	C₄×D₁₁₃	—	4	4	no	—
189	Dic₂₂₆	—	2	2	no	—
190	Dic₂₂₆	—	4	4	no	—
191	C₂²×C₁₁₃	—	2	1	no	—
192	C₂²×C₁₁₃	—	2	1	no	—
193	C₂²×C₁₁₃	—	2	1	no	—
194	C₂²×C₁₁₃	—	2	1	no	—
195	C₂²×C₁₁₃	—	2	1	no	—
196	C₂²×C₁₁₃	—	2	1	no	—
197	C₂²×C₁₁₃	—	2	1	no	—
198	C₂²×C₁₁₃	—	4	4	no	—
199	C₂²×C₁₁₃	C₂×#41	1	2	yes	—
200	C₂²×C₁₁₃	2₋¹⁺⁴	1	2	yes	—
201	C₂²×C₁₁₃	C₂⁵	1	1	yes	characteristic
202	C₂×D₁₁₃	—	2	2	no	—
203	C₂×D₁₁₃	—	2	2	no	—
204	C₂×D₁₁₃	—	2	2	no	—
205	C₄×C₁₁₃	—	2	1	no	—
206	C₄×C₁₁₃	—	2	1	no	—
207	C₄×C₁₁₃	—	2	4	no	—
208	C₄×C₁₁₃	—	2	4	no	—
209	C₄×C₁₁₃	C₂×#41	1	2	yes	—
210	C₄×C₁₁₃	C₂×#41	1	2	yes	—
211	Dic₁₁₃	—	2	2	no	—
212	Dic₁₁₃	—	2	2	no	—
213	Dic₁₁₃	—	2	2	no	—
214	Dic₁₁₃	—	2	2	no	—
215	Dic₁₁₃	—	2	2	no	—
216	Dic₁₁₃	—	2	2	no	—
217	Dic₁₁₃	—	2	2	no	—
218	C₂×C₁₁₃	—	2	2	no	—
219	C₂×C₁₁₃	—	2	2	no	—
220	C₂×C₁₁₃	—	4	1	no	—
221	C₂×C₁₁₃	C₂²×#41	1	1	yes	characteristic
222	C₂×C₁₁₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
223	C₂×C₁₁₃	#585	1	1	yes	characteristic
224	D₁₁₃	—	4	2	no	—
225	#3495	—	113	1	no	maximal, Sylow
226	C₁₁₃	#3495	1	1	yes	characteristic, complemented, Sylow
227	#556	—	113	2	no	—
228	#554	—	113	2	no	—
229	#552	—	113	2	no	—
230	#552	—	113	2	no	—
231	#552	—	113	4	no	—
232	#551	—	113	4	no	—
233	#544	—	113	1	no	—
234	#542	—	113	2	no	—
235	#541	—	113	2	no	—
236	#536	—	113	1	no	—
237	#533	—	113	2	no	—
238	#529	—	113	2	no	—
239	#525	—	113	1	no	—
240	C₂×C₂²⋊Q₈	D₁₁₃	1	1	yes	characteristic, complemented
241	#520	—	113	1	no	—
242	#519	—	113	1	no	—
243	C₂×#117	—	113	1	no	—
244	C₂×#41	—	113	1	no	—
245	C₂²×Q₈	C₂×D₁₁₃	1	1	yes	characteristic
246	C₂³×C₄	C₂×D₁₁₃	1	1	yes	characteristic
247	C₄⋊Q₈	—	113	2	no	—
248	C₄⋊Q₈	—	113	2	no	—
249	C₄⋊Q₈	—	113	2	no	—
250	#126	—	113	4	no	—
251	#126	—	113	4	no	—
252	#126	—	113	4	no	—
253	#126	—	113	4	no	—
254	#125	—	113	2	no	—
255	#125	—	113	4	no	—
256	#125	—	113	4	no	—
257	#125	—	113	4	no	—
258	#125	—	113	2	no	—
259	#124	—	113	2	no	—
260	#124	—	113	4	no	—
261	#123	—	113	2	no	—
262	#123	—	113	4	no	—
263	#123	—	113	4	no	—
264	#123	—	113	4	no	—
265	C₂²⋊Q₈	—	113	2	no	—
266	C₂²⋊Q₈	—	113	2	no	—
267	C₂²⋊Q₈	—	113	1	no	—
268	C₂²⋊Q₈	—	113	1	no	—
269	C₂²⋊Q₈	—	113	4	no	—
270	C₂²⋊Q₈	—	113	4	no	—
271	C₂²⋊Q₈	—	113	4	no	—
272	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	—
273	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	—
274	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	—
275	C₂²⋊Q₈	C₂×D₁₁₃	1	2	yes	—
276	#121	—	113	1	no	—
277	#121	—	113	1	no	—
278	#120	—	113	2	no	—
279	C₄×Q₈	—	113	2	no	—
280	C₄×Q₈	—	113	2	no	—
281	C₄×Q₈	—	113	2	no	—
282	C₄×Q₈	—	113	2	no	—
283	C₄×Q₈	—	113	2	no	—
284	C₄×Q₈	—	113	4	no	—
285	C₄×D₄	—	113	4	no	—
286	C₄×D₄	—	113	2	no	—
287	C₄×D₄	—	113	2	no	—
288	C₄×D₄	—	113	2	no	—
289	C₄×D₄	—	113	4	no	—
290	#117	—	113	1	no	—
291	#117	—	113	1	no	—
292	#117	—	113	2	no	—
293	#117	—	113	1	no	—
294	#117	—	113	2	no	—
295	#117	—	113	1	no	—
296	#117	—	113	1	no	—
297	#117	—	113	4	no	—
298	#117	—	113	2	no	—
299	#117	—	113	4	no	—
300	#117	—	113	4	no	—
301	C₂×C₄⋊C₄	—	113	1	no	—
302	C₂×C₄⋊C₄	—	113	1	no	—
303	C₂×C₄⋊C₄	—	113	2	no	—
304	C₂×C₄⋊C₄	C₂×D₁₁₃	1	1	yes	characteristic
305	C₂×C₄⋊C₄	C₂×D₁₁₃	1	2	yes	—
306	C₂×C₂²⋊C₄	—	113	2	no	—
307	C₂×C₂²⋊C₄	C₂×D₁₁₃	1	2	yes	—
308	C₂×C₄²	—	113	2	no	—
309	C₂⁴	C₂²×D₁₁₃	1	1	yes	characteristic
310	#41	—	226	4	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	—	113	4	no	—
313	C₂×Q₈	—	113	1	no	—
314	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
315	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
316	C₂×D₄	—	113	2	no	—
317	C₂×D₄	—	113	2	no	—
318	C₂×D₄	—	113	2	no	—
319	C₂×D₄	—	113	1	no	—
320	C₂²×C₄	—	2	4	no	—
321	C₂²×C₄	—	113	2	no	—
322	C₂²×C₄	—	113	2	no	—
323	C₂²×C₄	—	113	4	no	—
324	C₂²×C₄	—	113	2	no	—
325	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
326	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
327	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
328	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
329	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
330	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
331	C₂²×C₄	C₂²×D₁₁₃	1	2	yes	—
332	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
333	C₄⋊C₄	—	113	1	no	—
334	C₄⋊C₄	—	113	1	no	—
335	C₄⋊C₄	—	113	2	no	—
336	C₄⋊C₄	—	113	1	no	—
337	C₄⋊C₄	—	113	1	no	—
338	C₄⋊C₄	—	113	2	no	—
339	C₄⋊C₄	—	113	4	no	—
340	C₄⋊C₄	—	113	1	no	—
341	C₄⋊C₄	—	113	1	no	—
342	C₄⋊C₄	—	113	4	no	—
343	C₄⋊C₄	—	113	4	no	—
344	C₄⋊C₄	—	113	4	no	—
345	C₄⋊C₄	—	113	4	no	—
346	C₄⋊C₄	—	113	4	no	—
347	C₄⋊C₄	—	113	2	no	—
348	C₄⋊C₄	—	113	2	no	—
349	C₄⋊C₄	—	113	4	no	—
350	C₄⋊C₄	—	113	4	no	—
351	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
352	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
353	C₄⋊C₄	C₂²×D₁₁₃	1	2	yes	—
354	C₄⋊C₄	C₂²×D₁₁₃	1	4	yes	—
355	C₂²⋊C₄	—	113	2	no	—
356	C₂²⋊C₄	—	113	2	no	—
357	C₂²⋊C₄	—	113	2	no	—
358	C₂²⋊C₄	—	113	2	no	—
359	C₂²⋊C₄	—	113	2	no	—
360	C₂²⋊C₄	—	113	2	no	—
361	C₂²⋊C₄	—	113	2	no	—
362	C₂²⋊C₄	—	113	2	no	—
363	C₂²⋊C₄	—	113	4	no	—
364	C₂²⋊C₄	—	113	4	no	—
365	C₂²⋊C₄	—	113	2	no	—
366	C₂²⋊C₄	—	113	4	no	—
367	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
368	C₂²⋊C₄	C₂²×D₁₁₃	1	4	yes	—
369	C₄²	—	113	2	no	—
370	C₄²	—	113	2	no	—
371	C₄²	—	113	2	no	—
372	C₄²	—	113	2	no	—
373	C₄²	—	113	4	no	—
374	C₄²	—	113	4	no	—
375	C₄²	—	113	4	no	—
376	C₄²	—	113	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	4	1	no	—
380	C₂³	—	113	2	no	—
381	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
382	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
383	C₂³	C₂³×D₁₁₃	1	1	yes	characteristic
384	Q₈	—	2	4	no	—
385	Q₈	—	2	4	no	—
386	Q₈	—	452	4	no	—
387	Q₈	—	226	2	no	—
388	D₄	—	452	2	no	—
389	D₄	—	226	4	no	—
390	D₄	—	226	4	no	—
391	D₄	—	226	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	4	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	113	2	no	—
400	C₂×C₄	—	113	2	no	—
401	C₂×C₄	—	113	2	no	—
402	C₂×C₄	—	113	2	no	—
403	C₂×C₄	—	113	2	no	—
404	C₂×C₄	—	113	2	no	—
405	C₂×C₄	—	113	2	no	—
406	C₂×C₄	—	452	4	no	—
407	C₂×C₄	—	452	2	no	—
408	C₂×C₄	—	226	4	no	—
409	C₂×C₄	—	226	4	no	—
410	C₂×C₄	#14268646	1	4	yes	—
411	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
412	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
413	C₂×C₄	C₂³×D₁₁₃	1	4	yes	—
414	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
415	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
416	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	2	1	no	—
423	C₂²	—	2	1	no	—
424	C₂²	—	4	4	no	—
425	C₂²	—	226	2	no	—
426	C₂²	—	226	2	no	—
427	C₂²	—	226	2	no	—
428	C₂²	C₂×#14268646	1	2	yes	—
429	C₂²	#16813670	1	2	yes	—
430	C₂²	C₂⁴×D₁₁₃	1	1	yes	characteristic
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	4	no	—
434	C₄	—	2	4	no	—
435	C₄	—	226	2	no	—
436	C₄	—	226	2	no	—
437	C₄	—	226	2	no	—
438	C₄	—	226	2	no	—
439	C₄	—	226	2	no	—
440	C₄	—	226	2	no	—
441	C₄	—	226	2	no	—
442	C₄	C₂×#14268646	1	2	yes	—
443	C₄	C₂×#14268646	1	2	yes	—
444	C₂	—	2	2	no	—
445	C₂	—	2	2	no	—
446	C₂	—	4	1	no	—
447	C₂	—	452	2	no	—
448	C₂	C₂²×#14268646	1	1	yes	characteristic
449	C₂	C₂×#16813670	1	1	yes	characteristic
450	C₂	#20299434	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₁₃
commutator, socle, cosocle	C₂²×C₁₁₃	C₂⁵
Fitting	C₂×C₂²⋊Q₈×C₁₁₃	C₂
prime radical	#20299109	C₂
hypercenter	C₂×C₂²⋊Q₈	D₁₁₃
hypocenter	C₁₁₃	#3495
LCS	G ▷ C₂²×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂² ◁ C₂×C₂²⋊Q₈

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #20299319	C₂	semidirect
2. #20299306	C₂	semidirect
3. #20299290	C₂	semidirect
4. #20299283	C₂	semidirect
5. #20299282	C₂	semidirect
6. #20299274	C₂	semidirect
7. #20299229	C₂	semidirect
8. #20299221	C₂	semidirect
9. #20299208	C₂	semidirect
10. #20299172	C₂	semidirect
11. #20299150	C₂	semidirect
12. #20299134	C₂	semidirect
14. #20299079	C₂	semidirect
15. #20299076	C₂	semidirect
16. C₂×#16813581	C₂	semidirect
17. C₂×C₂²⋊Q₈×C₁₁₃	C₂	semidirect
19. #16813621	C₂²	semidirect
20. #16813621	C₂²	semidirect
21. #16813620	C₂²	semidirect
22. #16813617	C₂²	semidirect
23. #16813617	C₂²	semidirect
26. #16813613	C₂²	semidirect
27. #16813613	C₂²	semidirect
28. #16813613	C₂²	semidirect
29. #16813612	C₂²	semidirect
30. #16813612	C₂²	semidirect
31. #16813611	C₂²	semidirect
37. #16813602	C₂²	semidirect
42. #16813598	C₂²	semidirect
43. #16813598	C₂²	semidirect
47. Q₈×Dic₁₁₃	C₂²	semidirect
48. Q₈×Dic₁₁₃	C₂²	semidirect
49. Q₈×Dic₁₁₃	C₂²	semidirect
50. Q₈×Dic₁₁₃	C₂²	semidirect
51. #16813587	C₂²	semidirect
52. #16813587	C₂²	semidirect
53. #16813584	C₂²	semidirect
66. #16813580	C₂²	semidirect
67. #16813580	C₂²	semidirect
71. C₄⋊C₄×D₁₁₃	C₂²	semidirect
226. C₁₁₃	#3495	semidirect
240. C₂×C₂²⋊Q₈	D₁₁₃	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20299319	2
#20299306	2
#20299290	2
#20299283	2
#20299282	2
#20299274	2
#20299229	2
#20299221	2
#20299208	2
#20299172	2
#20299150	2
#20299134	2
#20299109	2
#20299079	2
#20299076	2
C₂×#16813581	2
C₂×C₂²⋊Q₈×C₁₁₃	2
#3495	113